a. Simple method to compute p ( x ) : Let us consider the “ p ( x ) ” polynomial of degree “n”. The method to compute the polynomial of degree is given below: //Define the simplePolynomial() method public static double simplePolynomial(double a[], double n) { //Declare the variable double sum = 0; //Loop executes until the length of array for(int i=0; i<a.length; i++) //Compute the polynomial of degree sum = sum + a[i] * Math.pow(n, a.length - i - 1); //Return the polynomial of degree return sum; } Running time: In the above code, the computation of polynomial of degree is given below: For each and every array term, a[0] is “0” operation. a [ 1 ] × x is “1” operation. a [ 2 ] × x × x is “2” operations. a [ 3 ] × x × x × x is “3” operations

Question

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Answer 1

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

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Students have asked these similar questions

Given an n-element array X of integers, Algorithm A executes an O(n) time computation for each even number in X and an O(log-n) time computation for each odd number in X. What are the best case and worst case for running time of algorithm C?

The order of growth of the function f(n)=2n×n is lower than the function g(n)= 2n×n2. Hence, f(n)=O(g(n)). Select one: a. None b. Yes c. No d. Maybe

Call a sequence X[1 · · n] of numbers oscillating if X[i] < X[i + 1] for all even i, and X[i] > X[i + 1] for all odd i. Describe an efficient algorithm to compute the length of the longest oscillating subsequence of an arbitrary array A of integers.

Answer 2

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 8

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Answer 9

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Answer 10

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Answer 11

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Answer 12

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 13

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 4 - Prob. 1R Ch. 4 - The number of operations executed by algorithms A...Ch. 4 - The number of operations executed by algorithms A...Ch. 4 - Prob. 4R Ch. 4 - Prob. 5R Ch. 4 - Prob. 6R Ch. 4 - Prob. 7R Ch. 4 - Prob. 8R Ch. 4 - Prob. 9R Ch. 4 - Prob. 10R

Solution Summary: The author explains the simple method to compute the polynomial of degree.

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Chapter 4 Solutions